Step |
Hyp |
Ref |
Expression |
1 |
|
2ndcomap.2 |
|
2 |
|
2ndcomap.3 |
|
3 |
|
2ndcomap.5 |
|
4 |
|
2ndcomap.6 |
|
5 |
|
2ndcomap.7 |
|
6 |
|
cntop2 |
|
7 |
3 6
|
syl |
|
8 |
7
|
ad2antrr |
|
9 |
|
simplll |
|
10 |
|
bastg |
|
11 |
10
|
ad2antlr |
|
12 |
|
simprr |
|
13 |
11 12
|
sseqtrd |
|
14 |
13
|
sselda |
|
15 |
9 14 5
|
syl2anc |
|
16 |
15
|
fmpttd |
|
17 |
16
|
frnd |
|
18 |
|
elunii |
|
19 |
18 1
|
eleqtrrdi |
|
20 |
19
|
ancoms |
|
21 |
20
|
adantl |
|
22 |
4
|
ad3antrrr |
|
23 |
21 22
|
eleqtrrd |
|
24 |
|
eqid |
|
25 |
24 1
|
cnf |
|
26 |
3 25
|
syl |
|
27 |
26
|
ad3antrrr |
|
28 |
|
ffn |
|
29 |
|
fvelrnb |
|
30 |
27 28 29
|
3syl |
|
31 |
23 30
|
mpbid |
|
32 |
3
|
ad3antrrr |
|
33 |
|
simprll |
|
34 |
|
cnima |
|
35 |
32 33 34
|
syl2anc |
|
36 |
12
|
adantr |
|
37 |
35 36
|
eleqtrrd |
|
38 |
|
simprrl |
|
39 |
|
simprrr |
|
40 |
|
simprlr |
|
41 |
39 40
|
eqeltrd |
|
42 |
27
|
ffnd |
|
43 |
42
|
adantrr |
|
44 |
|
elpreima |
|
45 |
43 44
|
syl |
|
46 |
38 41 45
|
mpbir2and |
|
47 |
|
tg2 |
|
48 |
37 46 47
|
syl2anc |
|
49 |
|
simprl |
|
50 |
|
eqid |
|
51 |
|
imaeq2 |
|
52 |
51
|
rspceeqv |
|
53 |
49 50 52
|
sylancl |
|
54 |
43
|
adantr |
|
55 |
|
fnfun |
|
56 |
54 55
|
syl |
|
57 |
|
simprrr |
|
58 |
|
funimass2 |
|
59 |
56 57 58
|
syl2anc |
|
60 |
|
vex |
|
61 |
|
ssexg |
|
62 |
59 60 61
|
sylancl |
|
63 |
|
eqid |
|
64 |
63
|
elrnmpt |
|
65 |
62 64
|
syl |
|
66 |
53 65
|
mpbird |
|
67 |
39
|
adantr |
|
68 |
|
simprrl |
|
69 |
|
cnvimass |
|
70 |
57 69
|
sstrdi |
|
71 |
|
funfvima2 |
|
72 |
56 70 71
|
syl2anc |
|
73 |
68 72
|
mpd |
|
74 |
67 73
|
eqeltrrd |
|
75 |
|
eleq2 |
|
76 |
|
sseq1 |
|
77 |
75 76
|
anbi12d |
|
78 |
77
|
rspcev |
|
79 |
66 74 59 78
|
syl12anc |
|
80 |
48 79
|
rexlimddv |
|
81 |
80
|
anassrs |
|
82 |
31 81
|
rexlimddv |
|
83 |
82
|
ralrimivva |
|
84 |
|
basgen2 |
|
85 |
8 17 83 84
|
syl3anc |
|
86 |
85 8
|
eqeltrd |
|
87 |
|
tgclb |
|
88 |
86 87
|
sylibr |
|
89 |
|
omelon |
|
90 |
|
simprl |
|
91 |
|
ondomen |
|
92 |
89 90 91
|
sylancr |
|
93 |
16
|
ffnd |
|
94 |
|
dffn4 |
|
95 |
93 94
|
sylib |
|
96 |
|
fodomnum |
|
97 |
92 95 96
|
sylc |
|
98 |
|
domtr |
|
99 |
97 90 98
|
syl2anc |
|
100 |
|
2ndci |
|
101 |
88 99 100
|
syl2anc |
|
102 |
85 101
|
eqeltrrd |
|
103 |
|
is2ndc |
|
104 |
2 103
|
sylib |
|
105 |
102 104
|
r19.29a |
|